When entire Young’s double slit apparatus is immersed in a liquid the fringe width decreases by 20%. The refractive index of liquid is:

On immersing the apparatus in water, the speed of wave travelling in water decreases and hence it’s wavelength decreases as v ∝ λ

Thus the new wavelength is 1/n times the the original wavelength since n=λ1/λ2

The fringe width originally is given by β1=λD/2d

The new fringe width within water will be given by β2=λD/2nd or β2=β1/n

Thus the fringe width decreases by a factor of n when immersed in water.

hence

for refrective index

n = 1 / (1 – 20/100) = 1 / (4/5) = 5/4

Regards

Arun (askIITians forum expert)